Steady-state distributions of water potential and salt concentration in coastal aquifers are typically illustrated by the Henry problem, which consists of a fully coupled system of flow and transport equations. Coupling is caused by the dependence of water density on salt concentration. While the Henry problem often serves as a benchmark for numerical codes, the accuracy of the existing numerical and approximate analytical solutions is hard to gauge. We provide a closed form formulation of the flow problem in terms of salt concentration and use a perturbation expansion in the coupling parameter to solve it analytically. The perturbation procedure results in a recursive set of flow and transport equations and their solutions that effectively decouples the two processes. This decoupling approach can be applied to a range of problems involving variable density fluids and sheds new light on coupled flow and transport mechanisms.